Unformatted text preview: “ β ”, (a) Find the dispersion relation ω (k) for phonons in the 1st BZ a k k k a z y x π ≤ ≤ − , , . (b) Using the relation β /M=Y/ ρ a 2 (Y: Young’s modulus = 1.14x10 11 Nt/m 2 , a=4.03Å, and ρ =2.73 g/cm 3 ), calculate the maximum phonon energy in electron volt (eV). (c) Calculate the speed of the sound in aluminum. 3. Assuming an E-k relation: ߝ ൌ ߝ మ మ 1 െ ܿݏ ቂቀ݇ െ గ ସ ቁ ܽቃ൨ . Plot the band diagram, the group velocity, and the effective mass over the first Brillouin Zone....
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- Fall '10
- Condensed matter physics, intrinsic carrier concentration, energy Eg,Ge=0.67 eV